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Duality theory for state-constrained control problems governed by a first order PDE system

Pickenhain S.

Control and Cybernetics

2002

Vol. 31, no 3

833-845

In this paper we prove weak and strong duality results for optimal control problems with multiple integrals, first-order partial differential equations and state constraints. We formulate conditions under which the sequence of canonical variables [y^epsilon] in the [epsilon]-maximum principle, proved in Pickenhain and Wagner (2000), form a maximizing sequence in the dual problem.

General method of relaxation. [Pt. 1], Functionals defined on BD(Omega) space

Bojarski J.

Bulletin of the Polish Academy of Sciences. Mathematics

1999

Vol. 47, no 3

289-301

The aim of this paper is to find the lower semicontinuous regularization of a functional of displacement energy, with a constrains on the boundary of Omega. This functional describes the elasto-perfectly plastic energy of a solid made of a nonhomogeneous (or homogeneous) Hencky material. In this contribution we prove that the mentioned above regularization is equal to the relaxation found in [4], i.e. B** = B#*.